OPTIMAL PORTFOLIO CHOICE WITH CRASH RISK AND MODEL AMBIGUITY

Abstract

In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for the investor, which also implies that there can be no crash at all. For the modeling of the parameter uncertainty, we choose a general definition of the sets of possible drift and volatility parameters, conditioned by the solution of an optimization problem. In addition, these sets may be different in the pre-crash and post-crash market. We solve this portfolio problem and then consider two particular examples with box uncertainty and ellipsoidal drift ambiguity.